Research areas Applied and numerical analysis of nonlinear partial differential equations; the construction and mathematical analysis of finite element approximations to nonlinear partial differential equations. In particular: Anisotropic and crystalline surface growth Cahn-Hilliard equation Double Obstacle Phase Field Free boundary problems Geometric evolution equations PDEs and Image Processing Numerical analysis and partial differential equations Surface Diffusion Surface Partial Differential Equation (PDEs on surfaces) Vortex density and critical state models for type II superconductors Unfitted Finite Element Method Viscosity Solutions, Hamilton Jacobi and eikonal equations